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The Law of Small Numbers

From an early Daniel Kahneman article referenced in Thinking Fast and Slow about how the poor instincts of researchers selecting samples can lead to undersampling:

“The law of large numbers guarantees that very large samples will indeed be highly representative of the population from which they are drawn. If, in addition, a self-corrective tendency is at work, then small samples should also be highly representative and similar to one another. People’s intuitions about random sampling appear to satisfy the law of small numbers, which asserts that the law of large numbers applies to small numbers as well.”*

Hint: it doesn’t apply. Based on the experience of reading numerous LIS studies and surveys, a lot of librarians implicitly believe in the law of small numbers. Of course, I might have just read an unrepresentative sample and they really don’t.

*Tversky, Amos, and Daniel Kahneman. “Belief in the Law of Small Numbers.” Psychological Bulletin 76, no. 2 (August 1971): 106.